Linear Regression and Simple Exponential Smoothing

Regression analysis is a method for investigating functional relationships among variables ( Chatterjee, & Hadi, 2012 ). The New Star Grocery Company believes that there may be a relationship between the number of customers who visit the store during any given month (“customer traffic”) and the total sales for that same month. They, therefore, decided to consult the Diligent Consulting Group where a regression analysis was conducted in order to determine the relationship between the two variables. The New Star Grocery Company decided to collect traffic data over the past 12-month period, and monthly sales for that same 12-month period. A linear regression analysis was conducted and using the linear regression equation, forecasting was done in order to determine the number of sales for the second year. 

A Linear Regression (LR) equation in Excel 

In carrying out a Linear Regression analysis, the data is first entered into an excel spreadsheet and in the following output and chart is obtained. 

Explanation 

The Linear Regression equation is y = 0.648x + 111.65. The dependent variable (response variable) in this case is the amount of sales whereas the predictor variable (independent variable) is the number of customers. This implies that the sales amount depends on the number of customers visiting the New Star Grocery Company. In other words, as the number of customers increases, the amount of sales also goes up and in the case of a decrease in the number of customers, the sales will also experience a deficit. The equation from the linear regression scatter plot indicates that the coefficient for sales in dollars is 111.65 dollars. This implies that for every additional dollar in height, one expects the amount of sales to increase by an average of 111.65 dollars. 

The fitted dotted line shows the same information graphically. If one moves along the x-axis by a measure that is representative of a one dollar change in a sale, the line either increases or decreases by 111.65 dollars depending on whether one is moving from (left or right). This information, however, implies to the sales of the New Star Grocery Company in the first year. In a scenario where the fitted dotted blue line was to be a flat line and not slanted like in this case, this would mean that the line equation has a coefficient of zero. Therefore, the expected sales would not increase or decrease in such a case. Taking a look at the regression output table, the R square value is 0.718 just like the one obtained in the scatter plot. The R-square is a measure of the strength of the values fitted in the regression line and in this case, there is a strong correlation between the number of customers and the amount of sales (Donnelly, & Abdel-Raouf, 2016) . Taking a look at the p-value, 0.01 and 0.0005 are both very low values and this suggests that any change in an independent variable (predictor variable) leads to change in the dependent variable (response variable). 

Forecasting 

Using the Linear Regression equation is y = 0.648x + 111.65, a forecast can be done in order to predict the amount of sales for the New Star Grocery company. The following table was obtained. 

Comparison between the actual year 2 sales and the forecasted year 2 sales 

A report for the client 

In order to obtain forecasted sales for year 2, the linear regression equation from module one was used. The new customer traffic for the second year was used as the new value of x and was substituted in the linear regression equation. For example, to obtain the first month’s sales for year two y = 0.648(215) + 111.65= 250.970. The total amount of sales obtained from the actual sales of year 2 is 3,513.33 dollars and the total sales for the forecasted sales 3354.432 dollars. The difference between forecast vs. actual sales for year 2 for the year as a whole is (3513.33-3354.432) =158.90 dollars. The difference between the monthly sales of the actual year 2 sales and the forecasted year 2 sales are provided in the table above. 

After using the regression equation, the obtained forecasted year 2 values are somewhat less than the actual sales. This implies that the linear regression equation gives a lower projection as to what might be the future sales. For instance, in the month of January, there is a variance of 23.30 dollars, for the month of February 13.26 dollars, however, the overall annual difference between the forecasted amount and the actual sales is approximately 159 dollars. 

I would, therefore, recommend that the New Star Grocery Company use the linear regression model to forecast their future sales as the difference obtained would be insignificant. I would recommend them to use the time series method of forecasting. Time series deals with four main components which are, trend, seasonal variation, cyclic variation and random components which work together in aiding the forecasting process ( Chatterjee, & Hadi, 2012 ). The time series analysis in linear regression would, therefore, assist the company efficiently since it can help in understanding past behavior or trend, help in planning for future operations and it also helps in facilitating comparisons. This will assist the New Star Grocery Company in assessing their profitability as they will be able to gauge their previous performance as well as their current sales performance. 

Conclusion 

Linear regression method is a simple yet convenient way of forecasting in business. It provides future values which may enable the New Star Grocery Company, in this case, to be able to plan ahead and make changes in order to increase their customer traffic. This is due to the fact that the company’s management noticed that more customers increase the amount of sales. Though the forecasted sales were a bit lower than the actual ones, the linear regression method still provided a good basis for gauging what the future sales might be. 

References

Chatterjee, S., & Hadi, A. (2012). Regression Analysis by Example (5th ed.). New Jersey: John Wiley & Sons. 

Donnelly, R., & Abdel-Raouf, F. (2016). Statistics (1st ed.). Indianapolis, Indiana: Alpha, a member of Penguin Random House LLC.